# Visualizing a 5x5x5 data set

I'm trying to visualize a matrix of 3 datasets.* For the sake of example, let's say I have a list of hats, coats and shoes, and I want to display a 2D grid/visualization of each possible combination.

Is it even possible without turning it into a 5x25 grid?

I had a look at this thread: Visualizing multi-dimensional data (LSI) in 2D, but from what I understand that one is about plotting as opposed to showing the fields in a grid/table of some sorts.

(*) I think i'm using the wrong terminology here, what I mean isn't about drawing points in a graph but rather a way to illustrate the data set in a meaningful matter that still allows for editing

Edit: This might explain what i'm trying to do:

    +------+------------+-------------+------------+
|      | hat        | shirt       | shoe       |
+------+------------+-------------+------------+
| red  | red hat    | red shirt   | red shoe   |
+------+------------+-------------+------------+
| blue | blue hat   | blue shirt  | blue shoe  |
+------+------------+-------------+------------+
|green | green hat  | green shirt | green shoe |
+------+------------+-------------+------------+
|black | black hat  | black short | black shoe |
+------+------------+-------------+------------+


... but with 3 data sets instead of just colors and clothes.

• To be sure to understand, the three datasets refer to different cross-classifications of two attributes? It may help if you could describe what's available in terms of number and type of variables (or attributes), number of statistical units, etc. – chl Jul 11 '11 at 21:42
• it could for instance be hats [fedora, fez and baseball cap], coats [long jacket, sports vest and blazer] and shoes [boots, flip flops and crocs]. What I was looking for was whether it was possible to have a grid or other visualization/chart containing each of the 3x3x3 combinations displayed, like the 3x4 above in my original post. I know i'm terrible at describing it - Sorry! :) – Frederik Jul 11 '11 at 21:48
• So, am I right in assuming we could have some statistical units, say $n_{ijk}$, being recorded as wearing baseball cap and blazer and boots (what's an awful combination!:-), etc? In this case, your question amounts to: What is the best solution to display a three-way contingency table? – chl Jul 11 '11 at 22:03
• Do you need to have this on paper or is it for an interactive visualization? – nico Jul 12 '11 at 5:56
• I need it on paper – Frederik Jul 12 '11 at 6:01

You could just have 5 rectangles, the the first being

+------+----------------------+------------------------+-----------------------+
|Babies| hat                  | shirt                  | shoe                  |
+------+----------------------+------------------------+-----------------------+
|red   | red hat for babies   | red shirt for babies   | red shoe for babies   |
+------+----------------------+------------------------+-----------------------+
|blue  | blue hat for babies  | blue shirt for babies  | blue shoe for babies  |
+------+----------------------+------------------------+-----------------------+
|green | green hat for babies | green shirt for babies | green shoe for babies |
+------+----------------------+------------------------+-----------------------+
|black | black hat for babies | black short for babies | black shoe for babies |
+------+----------------------+------------------------+-----------------------+


And the next being similar but being boys instead of babies, then girls, then men, then women.

Use a 2D plot, and use a color scale to represent the 3rd dimension. You could also try varying the symbol used to represent your points, or change the size of the marker.

• thanks @Zach, but I think I might not have been specific enough in my question - I've updated it to include a table "visualizing" what I meant, but with two data sets instead of three. Although using colors might have to be the way to go. I could have each cell contain 3 words, one for each color – Frederik Jul 11 '11 at 21:23